Masking a light for shadow texture
I think textured area lights are not fully supported yet. So currently one of the workarounds is to add another mesh under the lamp and add a transparent material on it with transparency controlled by the mask image (as seen below).



Another way is to add Texture Coordinates node to your existing area lamp material and connect the Reflection output to the Image Texture Vector input, however, that looks kinda strange and not very correct.